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Abstract
We obtain a basis of joint or proper differential invariants for the scalar linear hyperbolic partial differential equation in two independent variables by the infinitesimal method. The joint invariants of the hyperbolic equation consist of combinations of the coefficients of the equation and their derivatives which remain invariant under equivalence transformations of the equation and are useful for classification purposes. We also derive the operators of invariant differentiation for this type of equation. Furthermore, we show that the other differential invariants are functions of the elements of this basis via their invariant derivatives. Applications to hyperbolic equations that are reducible to their Lie canonical forms are provided.